ACT Math Practice Test 44 Questions with Verified Answers,100% CORRECT

ACT Math Practice Test 44 Questions with Verified Answers What is the sum of the first 4 terms of the arithmetic sequence in which the 6th term is 8 and the 10th term is 13 ? - CORRECT ANSWER 14.5 The solution set of which of the following equations is the set of real numbers that are 5 units from −3 ? | x + 5 | = −3 | x − 5 | = 3 | x + 5 | = 3 I x − 3 | = 5 | x + 3 | = 5 - CORRECT ANSWER | x + 3 | = 5 Which of the decimals −0.057, −0.57, −0.55, 0.073, 0.57 is the least? - CORRECT ANSWER -.57 For the fraction , assume that p is a prime number and q is not a multiple of p. For which of the following values of q will the decimal equivalent of be a repeating decimal with at least 1 nonzero digit that repeats? 200 80 65 40 25 - CORRECT ANSWER 65 Quadratic Formula - CORRECT ANSWER x = -b ± √(b² - 4ac)/2a Surface Area of a Cylinder - CORRECT ANSWER 2πrh+2πr² Volume of a cylinder - CORRECT ANSWER V=πr²h Surface area of a sphere - CORRECT ANSWER 4πr² Volume of a sphere - CORRECT ANSWER 4/3πr³ Discriminant - CORRECT ANSWER b^2-4ac nCr - CORRECT ANSWER order doesn't matter nPr - CORRECT ANSWER order does matter circle equation - CORRECT ANSWER (x-h)^2 + (y-k)^2 = r^2 ellipse equation - CORRECT ANSWER (x-h)^2/a^2 + (y-k)^2/b^2 = 1 sin^2x+cos^2x= - CORRECT ANSWER 1 sin graph - CORRECT ANSWER value of 0 at 0. cos graph - CORRECT ANSWER starts at 1 tangent graph - CORRECT ANSWER ALOHA Log rules - CORRECT ANSWER MA DS PM A package of 25 baseball cards sells for $2.00, and a package of 100 of the cards sells for $6.50. The cards in the larger package sell for how many cents less per card than the cards in the smaller package? 1/2 1 1/2 2 2 1/2 - CORRECT ANSWER 1 1/2 When 27 is divided by 6, the remainder is 3, and when 27 is divided by 7, the remainder is 6. What is the next greatest positive integer that has a remainder of 3 when divided by 6 and a remainder of 6 when divided by 7 ? 39 48 51 69 90 - CORRECT ANSWER 69 According to recent estimates, the Milky Way galaxy contains about 400 billion stars. Which of the following is 400 billion expressed in scientific notation? (Note: 1 billion = 1,000 million) 4 x 10^14 4 x 10^13 4 x 10^12 4 x 10^11 4 x 10^10 - CORRECT ANSWER 4 x 10^11 In a basketball passing drill, 5 basketball players stand evenly spaced around a circle. The player with the ball (the passer) passes it to another player (the receiver). The receiver cannot be the player to the passer's immediate right or left and cannot be the player who last passed the ball. A designated player begins the drill as the first passer. This player will be the receiver for the first time on which pass of the ball? 24th 10th 6th 5th 4th - CORRECT ANSWER 5th How many distinct real roots (solutions) does the equation x 4 - x = 0 have? 0 1 2 3 4 - CORRECT ANSWER 2 A movie was shown 6 times every day from November 24 through December 19. How many times was the movie shown in all? (Note: The month of November has 30 days.) - CORRECT ANSWER 156 If (3,5) is a point on the graph of the function f, then which of the following points must be on the graph of the inverse function f (-1) ? (−3,−5) (-1/3, -1/5) (1/3, 1/5) (2,4) (5,3) - CORRECT ANSWER (5,3) For any x and y, sin(x + y) = (sin x)(cos y) + (cos x)(sin y). Sin(π/2 + a) cos a -cos a sin a 1 + sin a 1 + a - CORRECT ANSWER cos a A stock's price is expected to vary between $10 and $20 over the next 6 months. It currently costs $12. If each possible value for the stock is equally likely to occur, then what is the theoretical probability that I will make money purchasing this stock? Pretend that stock prices can only be whole-dollar amounts. 73% 80% 100% 12% - CORRECT ANSWER 73% (First practice test #5) In 2015, the total rainfall in central city was 13 inches less than the total annual rainfall in central city in 2000. In 2016, the total rainfall was 33 inches greater than the total rainfall in 2000. If + indicates an increase in rainfall and - indicates a decrease, what was the difference, in inches, in the yearly rainfall from 2015 to 2016? -46 -20 +10 +20 +46 - CORRECT ANSWER +46 (First Practice Test 21) A park ranger records the height of a river at 7:00 am and 7:00 pm daily. On sunday at 7 pm the river was at a height of 14 feet. It fell at a rate of 1.5 feet per day from sunday at 7 pm through thursday at 7 pm. At that time heavy rains caused the water to rise at a constant rate of 3 feet per day. At what time will the park ranger first record a height of over 14 feet? Friday at 7pm Saturday at 7am Saturday at 7pm Sunday at 7am Sunday at 7pm - CORRECT ANSWER Sunday at 7am (First Practice test 31) If g(n)=-3/(n+2) and h(n)=-n, for what real value of x is g(x)=h(x)? 1 only 3 only -1 and 3 only 1 and -3 only 1 and 3 only - CORRECT ANSWER 1 and -3 only (First practice test 38) A teacher plans to use a 40 inch long roll of string to form a border around a rectangular space on her bulletin board reserved for student use. What is the maximum amount of space, in square inches, that she can reserve on her bulletin board? 96 99 100 160 400 - CORRECT ANSWER 100 (First practice test 40) A house painting company assigns three employees to a particular customers house. The first paints 3/7 of the house in her 4 hour shift. The second paints another 1/4 of the house before the third takes over. If they all paint at the same rate, how many hours will it take the third employee to finish painting the remainder of the house by himself? .32 2.00 3.00 3.63 9.33 - CORRECT ANSWER 3.00 (first practice test 48) For all real numbers (x,y and z), x<y<z, and xyz<0. Which of the following must be true? xy<yz x+y>y+z x/y<y/z x<yz x+z<y - CORRECT ANSWER x<yz (first practice test 49) A triangle has sides x, y, and z. x<y<z. Which of the following expressions could be used to find the measure of the smallest angle in the triangle. (Note that c²=a²+b²-2abcosC) *answer with the letter A. cos⁽⁻¹⁾(x²-y²-z²-2yz) B. cos⁽⁻¹⁾(z²-y²-x²-2xy) C. cos⁽⁻¹⁾(-(z²-y²-x²)/(2xy)) D. cos⁽⁻¹⁾(-(x²-y²-z²)/(2yz)) E. cos⁽⁻¹⁾(-(x²+y²-z²)/(2yz)) - CORRECT ANSWER D (first practice test 50) Kyle scores an average of p points per game in his first 9 basketball games of the season. After kyle scores n points in his 10th game, his season average increases by 3 points per game. What is the value of n-p? 3 12 27 30 39 - CORRECT ANSWER 30 (first practice test 52) The first term in sequence A is 6 and the third is 72. Which of the following equations could define sequence A for all positive values of n? 3(An−1)+2n 12(An−1) 6(An−1)+18n 6(An−1)-6 3(An−1)+2 - CORRECT ANSWER 3(An−1)+2n (first practice test 56) The set {13,7,22,6,4,a} has a mean of 11 and a median of b. If it can be determined, what is the value of a-b? -24 -4 4 24 cannot be determined - CORRECT ANSWER 4 (first practice test 57) A rectangular room has a width of n feet and a length of m, and n does not equal m. If they are both integers and the perimeter is 36 feet, which of the following cannot be the area of the room? 45 56 72 77 81 - CORRECT ANSWER 81 (first practice test 58) The equation (x-5)² + (y+2)²= 20 defines a circle that lies on the standard x,y coordinate plane, The line with endpoints (9,0) and (a,b) is a diameter of the circle. What is the value of a? -13 -7 -5 -2 1 - CORRECT ANSWER 1 In a recent survey, 14 people found their mayor to be "very competent." This number is exactly 20% of the people surveyed. How many people were surveyed? A. 28 B.35 C.56 D.70 E.84 - CORRECT ANSWER D.70 A train traveled at rate of 90 mph for x hours and then at a rate of 60 mph for y hours. Which expression represents the train's average rate in mph for the entire distance traveled? F.540/xy G.(90/x)*(60/y) H.(90/x)+(60/y) J.(90x+60y)/(x+y) K.150/(x+y) - CORRECT ANSWER J.(90x+60y)/(x+y) In a certain string ensemble, the ratio of men to women is 5:3. If there are a total of 24 people in the ensemble, how many women are there? A.12 B.11 C.10 D.9 E.8 - CORRECT ANSWER D.9 If x=/=0, and x^2-3x=6x, the x=? F.-9 G.-3 H.>3 J.3 K.9 - CORRECT ANSWER K.9